package euler.p001_050;

import euler.MainEuler;

public class Euler023 extends MainEuler {

    /*
        A perfect number is a number for which the sum
        of its proper divisors is exactly equal to the number.
        For example, the sum of the proper divisors of 28
        would be 1 + 2 + 4 + 7 + 14 = 28, which means that
        28 is a perfect number.

        A number n is called deficient if the sum of its
        proper divisors is less than n and it is called
        abundant if this sum exceeds n.

        As 12 is the smallest abundant number,
        1 + 2 + 3 + 4 + 6 = 16,
        the smallest number that can be written as
        the sum of two abundant numbers is 24.
        By mathematical analysis, it can be shown that
        all integers greater than 28123 can be written
        as the sum of two abundant numbers.
        However, this upper limit cannot be reduced
        any further by analysis even though it is known
        that the greatest number that cannot be expressed
        as the sum of two abundant numbers is less
        than this limit.

        Find the sum of all the positive integers which
        cannot be written as the sum of two abundant numbers
     */
    public String resolve() {
        boolean[] sumaAbundantes = new boolean[limite];
        primeHelper.isPrime(limite/2);
        for (int i= 1; i < limite/2; i++) {
            if (esAbundante(i)) {
                for (int j= i; j < limite; j++) {
                    if ((i+j<limite) && esAbundante(j)) {
                        sumaAbundantes[i+j]= true;
                    }
                }
            }
        }

        int suma = 0;
        for (int i = 1; i < limite; i++) {
            if (!sumaAbundantes[i]) {
                suma+=i;
            }
        }

        return String.valueOf(suma);
    }

    private static final int limite = 28124;
    private static int[] sumaDivisores = new int[limite];
    private boolean esAbundante(int n) {
        if (n < 1) {
            throw new IllegalArgumentException("Parametro menor que 1");
        }

        if (sumaDivisores[n] == 0) {
            if (n == 1) {
                sumaDivisores[1] = 1;

            } else if (primeHelper.isPrime(n)) {
                sumaDivisores[n] = n+1;

            } else {
                int suma = 0;
                for (int i: primeHelper.divisores(n)) {
                    suma+=i;
                }
                sumaDivisores[n] = suma;
            }
        }

        return sumaDivisores[n] > 2*n;
    }

}
